We denote the set of natural numbers
integers rational numbers and real numbers by N Z Q and R respectively.
The idea of convergence of a real sequence had been extended to statistical convergence by Fast (1951) and can also be found in Schoenberg (1959) If N denotes the set of natural numbers
and K [subset] N then K(m,n) denotes the cardinality of K [intersection] [m,n].
A map L:N [right arrow] N is defined by L(P, t) = card(tP[Intersection][Z.sup.d]), where card means the cardinality of (tP[Intersection][Z.sup.d]) and N is the set of natural numbers
. It is seen that L(P, t) can be represented as, L(P, t) = 1 + [SIGMA][c.sub.i][t.sup.i], this polynomial is said to be the Ehrhart polynomial of a lattice d polytope P.
where p, q [member of] N and N is the set of natural numbers
, Q is set of rational numbers.
First, the author includes zero in the set of natural numbers
First, we identified constructivist perspectives that have been, or could be used to describe thinking about infinite sets, specifically, the set of natural numbers
One would think that at least two numbers are necessary in order to build the full set of natural numbers
: zero and one.
Example : Let R be the set of Natural Numbers
including zero and [empty set] : R [right arrow] [0,1] be a fuzzy subset defined by
Then TWO chooses a subsequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of [x.sub.1] so that Im([k.sub.1]) is the set of natural numbers
which are divisible by 2, and not divisible by [2.sup.2].
One can obtain all k-power free number by the following method: From the set of natural numbers
(except 0 and 1).
S : N [right arrow] N, N, the set of natural numbers
such that S(1) = 1, and S(n)=The smallest integer such that n/S(n)!.
HN UN = N, where HN, the set of Happy Numbers, and UN, the set of Unhappy Numbers, and N, the set of Natural numbers